Given an array **arr[]** consisting of **N** elements and **Q** queries represented by **L**, **R**, and **K**. The task is to print the count of odd and even parity elements in the subarray **[L, R]** after Bitwise-XOR with K.

**Examples:**

Input:arr[] = {5, 2, 3, 1, 4, 8, 10}

query[] = {{0, 5, 3}, {1, 4, 8}, {4, 6, 10}}Output:

4 2

1 3

2 1Explanation:

In query 1, the odd and even parity elements in subarray [0:5] are [2, 1, 4, 8] and [5, 3]. Now after XOR with K = 3, the number of odd and even parity elements are 4 and 2 respectively.

In query 2, the odd and even parity elements in subarray [1:4] are [2, 1, 4] and [3]. Now after XOR with K = 8, the number of odd and even parity elements are 1 and 3 respectively.

In query 3, the odd and even parity elements in subarray [4:6] are [4, 8] and [10]. Now after XOR with K = 10, the number of odd and even parity elements are 2 and 1 respectively.

**Approach:** The idea is to use MO’s algorithm to pre-process all queries so that result of one query can be used in the next query.

- Sort all queries in a way that queries with L values from
**0 to √n – 1**are put together, followed by queries from**√n to 2 ×√n – 1**, and so on. All queries within a block are sorted in increasing order of R values. - Count the
**odd parity**elements and then calculate the**even parity**elements as

- Observation after XOR with odd and even parity elements:
- XOR of
**two odd parity**elements is an**even parity**element. - XOR of
**two even parity**elements is an**even parity**element. - XOR of
**one even parity**element and**another odd parity**element is an**odd parity**element and vice-versa.

- XOR of
- Process all queries one by one and increase the count of odd parity elements and now we will
**check the parity of K**. If**K**has an**even parity**then the count of**odd**and**even parity**remains the**same**else we**swap**them.- Let
**count_oddP**store the count of odd parity elements in previous query. - Remove extra elements of previous query and add new elements for the current query. For example, if previous query was [0, 8] and the current query is [3, 9], then remove the elements arr[0], arr[1] and arr[2] and add arr[9].

- Let
- In order to display the results, sort the queries in the order they were provided.

**Adding elements**

- If the current element has odd parity then increase the count of odd parity.

**Removing elements**

- If the current element has odd parity then decrease the count of odd parity.

Below is the implementation of the above approach:

## C++

`// C++ program to count odd and` `// even parity elements in subarray` `// after XOR with K` `#include <bits/stdc++.h>` `using` `namespace` `std;` `#define MAX 100000` `// Variable to represent block size.` `// This is made global so compare()` `// of sort can use it` `int` `block;` `// Structure to represent` `// a query range` `struct` `Query {` ` ` `// Starting index` ` ` `int` `L, R, K, index;` ` ` `// Count of odd` ` ` `// parity elements` ` ` `int` `odd;` ` ` `// Count of even` ` ` `// parity elements` ` ` `int` `even;` `};` `// To store the count of` `// odd parity elements` `int` `count_oddP;` `// Function used to sort all queries so that` `// all queries of the same block are arranged` `// together and within a block, queries are` `// sorted in increasing order of R values.` `bool` `compare(Query x, Query y)` `{` ` ` `// Different blocks, sort by block.` ` ` `if` `(x.L / block != y.L / block)` ` ` `return` `x.L / block < y.L / block;` ` ` `// Same block, sort by R value` ` ` `return` `x.R < y.R;` `}` `// Function used to sort all queries` `// in order of their index value so` `// that results of queries can be` `// printed in same order as of input` `bool` `compare1(Query x, Query y)` `{` ` ` `return` `x.index < y.index;` `}` `// Function to Add elements` `// of current range` `void` `add(` `int` `currL, ` `int` `a[])` `{` ` ` `// _builtin_parity(x)returns true(1)` ` ` `// if the number has odd parity else` ` ` `// it returns false(0) for even parity.` ` ` `if` `(__builtin_parity(a[currL]))` ` ` `count_oddP++;` `}` `// Function to remove elements` `// of previous range` `void` `remove` `(` `int` `currR, ` `int` `a[])` `{` ` ` `// _builtin_parity(x)returns true(1)` ` ` `// if the number has odd parity else` ` ` `// it returns false(0) for even parity.` ` ` `if` `(__builtin_parity(a[currR]))` ` ` `count_oddP--;` `}` `// Function to generate the result of queries` `void` `queryResults(` `int` `a[], ` `int` `n, Query q[],` ` ` `int` `m)` `{` ` ` `// Initialize number of odd parity` ` ` `// elements to 0` ` ` `count_oddP = 0;` ` ` `// Find block size` ` ` `block = (` `int` `)` `sqrt` `(n);` ` ` `// Sort all queries so that queries of` ` ` `// same blocks are arranged together.` ` ` `sort(q, q + m, compare);` ` ` `// Initialize current L, current R and` ` ` `// current result` ` ` `int` `currL = 0, currR = 0;` ` ` `for` `(` `int` `i = 0; i < m; i++) {` ` ` `// L and R values of current range` ` ` `int` `L = q[i].L,` ` ` `R = q[i].R,` ` ` `k = q[i].K;` ` ` `// Add Elements of current range` ` ` `while` `(currR <= R) {` ` ` `add(currR, a);` ` ` `currR++;` ` ` `}` ` ` `while` `(currL > L) {` ` ` `add(currL - 1, a);` ` ` `currL--;` ` ` `}` ` ` `// Remove element of previous range` ` ` `while` `(currR > R + 1)` ` ` `{` ` ` `remove` `(currR - 1, a);` ` ` `currR--;` ` ` `}` ` ` `while` `(currL < L) {` ` ` `remove` `(currL, a);` ` ` `currL++;` ` ` `}` ` ` `// If parity of K is even` ` ` `// then the count of odd` ` ` `// and even parity remains` ` ` `// the same` ` ` `if` `(!__builtin_parity(k)) {` ` ` `q[i].odd = count_oddP;` ` ` `q[i].even` ` ` `= R - L + 1 - count_oddP;` ` ` `}` ` ` `// If parity of K is odd` ` ` `// we swap the count of` ` ` `// odd and even parity` ` ` `// elements` ` ` `else` `{` ` ` `q[i].odd` ` ` `= R - L + 1 - count_oddP;` ` ` `q[i].even = count_oddP;` ` ` `}` ` ` `}` `}` `// Function to display the results of` `// queries in their initial order` `void` `printResults(Query q[], ` `int` `m)` `{` ` ` `sort(q, q + m, compare1);` ` ` `for` `(` `int` `i = 0; i < m; i++) {` ` ` `cout << q[i].odd << ` `" "` ` ` `<< q[i].even << endl;` ` ` `}` `}` `// Driver Code` `int` `main()` `{` ` ` `int` `arr[] = { 5, 2, 3, 1, 4, 8, 10 };` ` ` `int` `n = ` `sizeof` `(arr) / ` `sizeof` `(arr[0]);` ` ` `Query q[] = { { 0, 5, 3, 0, 0, 0 },` ` ` `{ 1, 4, 8, 1, 0, 0 },` ` ` `{ 4, 6, 10, 2, 0, 0 } };` ` ` `int` `m = ` `sizeof` `(q) / ` `sizeof` `(q[0]);` ` ` `queryResults(arr, n, q, m);` ` ` `printResults(q, m);` ` ` `return` `0;` `}` |

## Java

`// Java program to count odd and` `// even parity elements in subarray` `// after XOR with K` `import` `java.io.*;` `import` `java.util.*;` `// Class to represent` `// a query range` `class` `Query` `{` ` ` `int` `L, R, K, index;` ` ` `// Count of odd` ` ` `// parity elements` ` ` `int` `odd;` ` ` `// Count of even` ` ` `// parity elements` ` ` `int` `even;` ` ` `Query(` `int` `L, ` `int` `R, ` `int` `K,` ` ` `int` `index, ` `int` `odd, ` `int` `even)` ` ` `{` ` ` `this` `.L = L;` ` ` `this` `.R = R;` ` ` `this` `.K = K;` ` ` `this` `.index = index;` ` ` `this` `.odd = odd;` ` ` `this` `.even = even;` ` ` `}` `}` `class` `GFG{` `// Variable to represent block size.` `static` `int` `block;` `// To store the count of` `// odd parity elements` `static` `int` `count_oddP;` `// Function to Add elements` `// of current range` `static` `void` `add(` `int` `currL, ` `int` `a[])` `{` ` ` ` ` `// _builtin_parity(x)returns true` ` ` `// if the number has odd parity else` ` ` `// it returns false for even parity.` ` ` `if` `(__builtin_parity(a[currL]))` ` ` `count_oddP++;` `}` `// Function to remove elements` `// of previous range` `static` `void` `remove(` `int` `currR, ` `int` `a[])` `{` ` ` ` ` `// _builtin_parity(x)returns true` ` ` `// if the number has odd parity else` ` ` `// it returns false for even parity.` ` ` `if` `(__builtin_parity(a[currR]))` ` ` `count_oddP--;` `}` `// Function to generate the result of queries` `static` `void` `queryResults(` `int` `a[], ` `int` `n, Query q[],` ` ` `int` `m)` `{` ` ` ` ` `// Initialize number of odd parity` ` ` `// elements to 0` ` ` `count_oddP = ` `0` `;` ` ` `// Find block size` ` ` `block = (` `int` `)(Math.sqrt(n));` ` ` `// sort all queries so that all queries` ` ` `// of the same block are arranged together` ` ` `// and within a block, queries are sorted` ` ` `// in increasing order of R values.` ` ` `Arrays.sort(q, (Query x, Query y) ->` ` ` `{` ` ` ` ` `// Different blocks, sort by block.` ` ` `if` `(x.L / block != y.L / block)` ` ` `return` `x.L / block - y.L / block;` ` ` `// Same block, sort by R value` ` ` `return` `x.R - y.R;` ` ` `});` ` ` `// Initialize current L, current R and` ` ` `// current result` ` ` `int` `currL = ` `0` `, currR = ` `0` `;` ` ` `for` `(` `int` `i = ` `0` `; i < m; i++)` ` ` `{` ` ` ` ` `// L and R values of current range` ` ` `int` `L = q[i].L, R = q[i].R, k = q[i].K;` ` ` `// Add Elements of current range` ` ` `while` `(currR <= R)` ` ` `{` ` ` `add(currR, a);` ` ` `currR++;` ` ` `}` ` ` `while` `(currL > L)` ` ` `{` ` ` `add(currL - ` `1` `, a);` ` ` `currL--;` ` ` `}` ` ` `// Remove element of previous range` ` ` `while` `(currR > R + ` `1` `)` ` ` `{` ` ` `remove(currR - ` `1` `, a);` ` ` `currR--;` ` ` `}` ` ` `while` `(currL < L)` ` ` `{` ` ` `remove(currL, a);` ` ` `currL++;` ` ` `}` ` ` `// If parity of K is even` ` ` `// then the count of odd` ` ` `// and even parity remains` ` ` `// the same` ` ` `if` `(!__builtin_parity(k))` ` ` `{` ` ` `q[i].odd = count_oddP;` ` ` `q[i].even = R - L + ` `1` `- count_oddP;` ` ` `}` ` ` ` ` `// If parity of K is odd` ` ` `// we swap the count of` ` ` `// odd and even parity` ` ` `// elements` ` ` `else` ` ` `{` ` ` `q[i].odd = R - L + ` `1` `- count_oddP;` ` ` `q[i].even = count_oddP;` ` ` `}` ` ` `}` `}` `static` `boolean` `__builtin_parity(` `int` `K)` `{` ` ` `return` `(Integer.bitCount(K) % ` `2` `) == ` `1` `;` `}` `// Function to display the results of` `// queries in their initial order` `static` `void` `printResults(Query q[], ` `int` `m)` `{` ` ` `Arrays.sort(q, (Query x, Query y) ->` ` ` `// sort all queries` ` ` `// in order of their` ` ` `// index value so that results` ` ` `// of queries can be printed` ` ` `// in same order as of input);` ` ` `x.index - y.index);` ` ` `for` `(` `int` `i = ` `0` `; i < m; i++)` ` ` `{` ` ` `System.out.println(q[i].odd + ` `" "` `+` ` ` `q[i].even);` ` ` `}` `}` `// Driver Code` `public` `static` `void` `main(String[] args)` `{` ` ` `int` `arr[] = { ` `5` `, ` `2` `, ` `3` `, ` `1` `, ` `4` `, ` `8` `, ` `10` `};` ` ` `int` `n = arr.length;` ` ` `Query q[] = ` `new` `Query[` `3` `];` ` ` `q[` `0` `] = ` `new` `Query(` `0` `, ` `5` `, ` `3` `, ` `0` `, ` `0` `, ` `0` `);` ` ` `q[` `1` `] = ` `new` `Query(` `1` `, ` `4` `, ` `8` `, ` `1` `, ` `0` `, ` `0` `);` ` ` `q[` `2` `] = ` `new` `Query(` `4` `, ` `6` `, ` `10` `, ` `2` `, ` `0` `, ` `0` `);` ` ` `int` `m = q.length;` ` ` `queryResults(arr, n, q, m);` ` ` `printResults(q, m);` `}` `}` `// This code is contributed by jithin` |

**Output:**

4 2 1 3 2 1

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